My Character’s Armature keeps flying off the screen
This is probably happening because your character has a static physics type..

Just select the character (mesh) and set its physics to "No Collision"



A better setup would be as follow :


Main character mesh - Physics : No Collision.
Armature - Physics : No Collision.
Add a mesh representing the character collision box - Physics : Character or whatever you like!
Parent the armature to the collision box and that's it!


The armature would control the animations (actions) and the collision box would control everything else